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    $\begingroup$ I haven't given this any thought, but I'd like to point out a couple of feelings. 1) I value (don't ask why) that compositions remain unevaluated if they are not applied to something, instead of turning into a Function. 2) When I read your question, I thought the natural way it should work was a different one (don't ask why, and I DONT THINK it would be beneficial. I just assumed it more natural). Namely, that doing (f@*g)[x] would be like inputting x to g, and then giving the output to f. So for ex, if h holds, (f@*h)[2+2] would give f[h[2+2]], but (h@*f)[2+2] would give h[f[4]]. $\endgroup$ Commented Jul 14, 2014 at 17:00
  • $\begingroup$ @Rojo The only way I know to keep comp[. . .] unevaluated is to make use of Leonid's Stack[_] method in the linked answer; I'll post an implementation of that when I have time. As to your natural way: that is actually what I was thinking when I write the line that is now struck out in the Question, but then thought "no, that's not right." Perhaps that functionality should also be considered or explored? $\endgroup$ Commented Jul 14, 2014 at 23:41